Stephanie is 12 years younger than Jessica. Jessica and Stephanie first met 3 years ago. Fifteen years ago, Jessica was 3 times as old as Stephanie. How old is Jessica now?
Solution: We can use the given information to write down two equations that describe the ages of Jessica and Stephanie. Let Jessica's current age be $j$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $j = s + 12$ Fifteen years ago, Jessica was $j - 15$ years old, and Stephanie was $s - 15$ years old. The information in the second sentence can be expressed in the following equation: $j - 15 = 3(s - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $s$ and substitute it into our second equation. Solving our first equation for $s$ , we get: $s = j - 12$ . Substituting this into our second equation, we get the equation: $j - 15 = 3($ $(j - 12)$ $ -$ $ 15)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 15 = 3j - 81$ Solving for $j$ , we get: $2 j = 66$ $j = 33$.